The trust needs to cut spending by £64m by 2017. The union Unison said it wants a full inquiry into the project.

The report added that doubts over the trust's ability to meet repayments without services suffering had been raised but ignored before construction began in 2007.

The hospital was officially opened by the Duke and Duchess of Cambridge on Wednesday,

It has been acknowledged that our PFI payments are unaffordableDr Peter Reading, Interim chief executive of hospital trust

'Critical financial position'

Amyas Morse, head of the NAO, called for "urgent action" from the trust, the Department of Health and regulators to "get the trust back on its feet".

He added: "The trust board's poor financial management and procurement of an unaffordable PFI scheme have left the trust in a critical financial position.

"The board developed and enthusiastically supported an unrealistic business case built on over-optimistic financial projections.

"The regulatory and approval processes did not work in this case and did not ensure affordability."

Last year, the trust faced a deficit of £46m, which is expected to rise to £50m this year.

This is as a result of the PFI scheme, past financial failings and other changes affecting the hospital's income.

The capital cost of the scheme as a proportion of turnover was the largest in the NHS, at 142%.

Monitor, the regulator of foundation trusts, raised concerns about the scheme's affordability before it was approved.

But neither the trust board nor the Department of Health addressed these concerns fully, the NAO said.

'Went badly wrong'

Dr Peter Reading, interim chief executive of the hospital trust, said the board acknowledged shortcomings but had put in place "new structures and systems to improve our financial forecasting".

He said the trust was on track to deliver £13.2m cost savings in 2012-13.

"It has been acknowledged that our PFI payments are unaffordable," he said. "As the majority of the board members who approved the project to build our hospital are no longer in post, I cannot speak on their behalf about the decisions taken at the time."

Dr David Bennett, Monitor chief executive, said the organisation had queried the affordability of the PFI scheme from the start, "but the trust went ahead with the PFI anyway".

"Once the financial situation at Peterborough became clear, Monitor took regulatory action, and we continue to work closely with the trust, along with commissioners and the Department of Health, to turn around its financial performance."

A Department of Health spokesman said it the case was an example of where "PFI policy went badly wrong".

Tracey Lambert, from Unison, said: "A hospital which originally cost £310m will end up costing the taxpayer £1.6 billion.

"Even mortgage finance at 6% would be far cheaper than the soaring cost of PFI.

"But to make sure we get a change of policy, we want to expose to public view just what was done in Peterborough, who signed off the deal and who rubber-stamped it."